off the top of their head what the difference between an epimorphism and a hylomorphism is?
They're not even from the same branch of mathematics. Epimorphisms are defined in category theory, as arrows which can be cancelled when they appear on the right of a composite, that is, if f is an epimorphism, and g . f = h . f, then g = h. Such arrows are somewhat comparable to surjective functions. Hylomorphisms are from recursion theory. They are the composite of an anamorphism (which builds up a recursive structure from an initial seed) with a catamorphism, (which replaces the constructors in that recursive structure with other functions). Terminology has value, in that it allows you to see things in a new way which is clearer than what could otherwise be achieved. Any programmer worth their salt should be comfortable absorbing a new term, the same way they learn a new library function. We should remember that Haskell's beauty is not an accident. It is proportional to the amount of effort which went into building the solid mathematical foundations describing its semantics, and designing a language which reflected those semantics as clearly as possible. Discarding those foundations in an attempt to get more users is a price I would personally never want to see us pay. - Cale